Estimation procedures for grouped data – a comparative study

ABSTRACT

Interval-censored data are very common in the reliability and lifetime data analysis. This paper investigates the performance of different estimation procedures for a special type of interval-censored data, i.e. grouped data, from three widely used lifetime distributions. The approaches considered here include the maximum likelihood estimation, the minimum distance estimation based on chi-square criterion, the moment estimation based on imputation (IM) method and an ad hoc estimation procedure. Although IM-based techniques are extensively used recently, we show that this method is not always effective. It is found that the ad hoc estimation procedure is equivalent to the minimum distance estimation with another distance metric and more effective in the simulation. The procedures of different approaches are presented and their performances are investigated by Monte Carlo simulation for various combinations of sample sizes and parameter settings. The numerical results provide guidelines to analyse grouped data for practitioners when they need to choose a good estimation approach.

KEYWORDS:

• Grouped data
• imputation algorithm
• interval-censored data
• lognormal distribution
• minimum distance estimation
• Weibull distribution

Acknowledgment

The second author is grateful to City University of Hong Kong for funding his visit during early part of this work. We also would like to thank the editor and referees for their comments that helped to improve an earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 9380058) and a grant from National Natural Science Foundation of China (No. 71371163).